Answer
$8+2\sqrt{15}$
Work Step by Step
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the given expression, $
(\sqrt{3}+\sqrt{5})^2
,$ is equivalent to
\begin{align*}
&
(\sqrt{3})^2+2(\sqrt{3})(\sqrt{5})+(\sqrt{5})^2
\\&=
3+2\sqrt{15}+5
\\&=
8+2\sqrt{15}
.\end{align*}
Hence, the product of the given expression is $
8+2\sqrt{15}
$.
